| The concepts of entanglement and superpositions introduced by quantum mechanics promise to allow for the design of a new computing architecture, called a quantum computer, that can exponentially outperform any possible classical computer. Such a performance improvement would make presently intractable computational problems efficiently solvable. Such problems include optimizations, like the traveling salesman problem, factorization, and quantum simulations, e.g. for medical research.;This thesis discusses one approach to implementing a quantum computer that is based on Superconducting Josephson Phase Qubits. An experiment is presented that shows a violation of Bell's inequality using these qubits (quantum bits), i.e. it demonstrates that a pair of these qubits can be placed into a state that shows a stronger correlation than possible for a classical pair of bits. This experiment meets a major mile-stone for the field of superconducting qubits as it provides strong evidence that the architecture will indeed be able to outperform classical systems.;Furthermore, this experiment is the first demonstration of a violation of Bell's inequality in a solid state system, and the first demonstration in a macroscopic quantum system. It therefore adds valuable supporting evidence that the new ideas proposed by quantum mechanics are indeed valid across different quantum systems and cannot be explained by a deterministic alternative theory. |